theorem Th61:
  for A, t, u st A, GRZ-rules |- t & A, GRZ-rules |- t '=' u holds
      A, GRZ-rules |- u
proof
  let A, t, u;
  assume A1: A, GRZ-rules |- t & A, GRZ-rules |- t '=' u;
  set S = {t, t '=' u};
  for a st a in S holds a in GRZ-formula-set
    proof
    let a;
    assume a in S;
    then a = t or a = t '=' u by TARSKI:def 2;
    hence thesis;
    end;
  then S c= GRZ-formula-set;
  then reconsider S as GRZ-formula-finset;
  A3: A, GRZ-rules |- S by A1, TARSKI:def 2;
  [S, u] in GRZ-MP;
  then [S, u] in GRZ-rules by Def35;
  hence A, GRZ-rules |- u by A3, Th48;
end;
